If the mean of $100$ observations is $50$ and their standard deviation is $5$,then the sum of squares of all observations is

The variance of $20$ observations is $5$. If each of the observations is multiplied by $2$,then the variance of the resulting observations is:

The following is the record of goals scored by team $A$ in a football session:

No. of goals scored	$0, 1, 2, 3, 4$
No. of matches	$1, 9, 7, 5, 3$

For team $B$,the mean number of goals scored per match was $2$ with a standard deviation of $1.25$ goals. Find which team may be considered more consistent?

Two dice $A$ and $B$ are rolled. Let the numbers obtained on $A$ and $B$ be $\alpha$ and $\beta$ respectively. If the variance of $\alpha - \beta$ is $\frac{p}{q}$,where $p$ and $q$ are coprime,then the sum of the positive divisors of $p$ is equal to

Given that $\bar{x}$ is the mean and $\sigma^{2}$ is the variance of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$,prove that the mean and variance of the observations $a x_{1}, a x_{2}, \ldots, a x_{n}$ are $a \bar{x}$ and $a^{2} \sigma^{2}$ respectively,where $a \neq 0$.

What is the standard deviation of the numbers $31, 32, 33, \dots, 47$?